The
more standard axiomatization of RI uses B / Syl* =
CCpqCCrpCrq / (p→q)→((r→p)→(r→q))
in place of B' / Syl (whence the common alternate name "BCIW"
for RI).Of course B' and B are
interdeducible in the presence of C, but in my experience
B' has seemed to be more generally useful in obtaining proofs of
other results than B in a variety of settings.
Anderson and Belnap ask [Entailment:
the logic of relevance and necessity, Princeton University
Press, Princeton, 1975] if there exists a single axiom for
RI, and the question was answered affirmatively by Rezus[On a theorem of Tarski, Libertas mathematica, vol. 2 (1982), pp. 63-9], who showed
how to construct (but did not actually display) such an axiom.
Written out in full, the Rezus axiom developed from the base
shown above is of type <93, 23>, that is, is 93 symbols in
length and contains occurrences of 23 distinct sentence letters: